Is language understanding possible without qualia?
I'm going to be controversial here; so please don't vote this answer down if you just disagree with it.

Your question presupposes that machines do not or cannot possess qualia, which are required for true understanding. Given that we don't really know what it means to 'understand' something, and that even the meaning of 'meaning' itself is by no means a resolved issue, it might be overly specific.

In one strand of linguistics, the meaning of a word is defined by its use, and by the context of surrounding words. We could hazard a guess that children acquire the meaning of words through exposure to language, and the correlation of experiences with the corresponding sounds. How that works in detail is AFAIK not fully understood. But there would be nothing 'inherent' in a new-born human that would enable it to 'understand' anything.

If that is the case, then we could train a machine to do the same. Obviously, it would be a long and tedious process, and there is probably a reason why it takes us years to become proficient in our use of language. But if we correlate sensory input with linguistic utterances, a sufficiently sophisticated learning algorithm might be able to acquire some meaning for such utterances from the way they are used.

There are, of course, rather a lot of unknowns here. That is because the topic straddles various fields, from child language acquisition, corpus linguistics, the psychology of learning, and many more. And to my knowledge, none of these fields is sufficiently advanced to shed any light on this issue yet. There is the whole question of abstract words and concepts. How do we segment the continuous stream of sounds into discrete units (phonemes) without knowing what they are? With all that complexity I begin to appreciate why Chomsky opted for his Language Acquisition Device to avoid getting frustrated... :)

So, to answer your question: yes, it should be possible. A properly set up machine, which would be able to simulate human learning, would pick up its own mapping of linguistic structures to its experience from the world outside. And if we call this mapping the 'meaning' of those structures, then a machine can learn this, and presumably 'understand' language. If we ever get to that stage with AI is another question.